Stat 543 Assignment 5
(not to be collected, but fair game on Exam I, February 21, 2005)
Maximum Likelihood, E-M Algorithm, (SEL) Bayes Estimation
1. Problems: 2.2.30, 2.2.35, 2.2.39
2. As in the first problem on Assignment 1, suppose that X1 , X2 , . . . , X10 are iid exponential with mean θ. That is, suppose that the marginal pdf is
³ x´
1
f (x|θ) = I [x ≥ 0] exp −
θ
θ
Suppose further that what is observed is not the Xi , but rather Y1 , Y2 , . . . , Y10 for
Yi = Xi rounded to the nearest integer
Write out an E-M algorithm for finding the MLE of θ based on the the available data.
3. Write out an E-M algorithm for finding the MLE of p based on all data collected in
the three studies mentioned in the 3rd problem of Assignment 1.
4. Problems 3.2.1, 3.2.2, 3.2.3, 3.2.4
1